Friday, March 25, 2011

Indeterminacy: Farmer and Kocherlakota

I ran across this, which appears to be a conference presentation by Kocherlakota. He's not quite in central banker mode here (though there is a bit of that in the paper). It seems he's still doing research, and wants to tell us about it.

A paper that Narayana gives high praise to is this one, by Roger Farmer (UCLA). Roger is another person who does not have much time for research these days, as he is currently chairing UCLA's economics department. Roger once told me about the paper, but I have never read it, so thought I would take a look. Roger calls this an "Old Keynesian" model, which I think is accurate. There are no sticky prices and wages in sight, and this is in the spirit of models with indeterminacies, going back to John Bryant, Peter Diamond, and, as some people would have it, Keynes himself. Roger, Jess Benhabib, Mike Woodford, Russ Cooper, and others developed dynamic, quantitative versions of models with indeterminacies, but the Keynesian models that Woodford ultimately marketed to the profession and central bankers were not those ones. New Keynesian models have uniqueness, and are more in the neoclassical growth model tradition - essentially RBC models with monopolistic competition and sticky prices.

So what is going on in Roger's model? At first you think he might just be re-doing Peter Diamond. There is search and matching in the labor market, but he does not appear to be generating indeterminacies through increasing returns in the matching function, as Diamond does. Further, it seems that if firms and workers bargain over wages in the the usual Diamond-Mortensen-Pissarides Nash bargaining fashion, that we get determinacy. Further, it's apparently not sunspot indeterminacy either, as in the Farmer/Benhabib/Woodford type models. There seems to be something exogenous in there, which Roger interprets as beliefs or animal spirits, which is driving asset prices. The asset prices are apparently determined in the usual forward-looking manner, but I wasn't sure whether these beliefs were ultimately self-fulfilling or not.

In any event, apparently beliefs drive the equilibrium outcome, and we could be stuck in a high unemployment state with low asset prices. Ultimately, though, I'm not sure I understood everything correctly. Maybe someone can help me out. Further, Roger seems to want to connect his model to current events, but he might have trouble explaining why the stock market is doing well, real GDP growth is sort of OK, and the labor market is still in the toilet.

Anwyay, back to Narayana's model, which is here. The ideas seem to be coupled to his discussion of a Kiyotaki-Moore paper at this conference (see Narayana's slides, which are linked in the program). In that discussion, Narayana discusses bubbles, which in his context are essentially the types of equilibria that we are accustomed to studying in monetary models. Fiat money can have value in equilibrium, in spite of the fact that its fundamental value is zero - there is a money bubble. However, there is always an equilibrium where the bubble bursts: money will have zero value if everyone expects it to.

Narayana couples the bubble idea to a Diamond/Mortensen/Pissarides search environment, and then uses Farmer's idea to get the indeterminacy. Then he tries to get the central bank to move the real interest rate around to select among the equilibria and get us out of the low unemployment state. Two problems here: (i) We want a more serious treatment of central banking. It may be the case that monetary policy can move the real rate, but we want to know why. That's critical. (ii) Narayana (and Farmer too) slip into "aggregate demand" language. If we go back through the history of thought, we find Woodford and Peter Diamond doing it too. Why is this a mistake? "Aggregate demand" and "aggregate supply" is a language associated with a particular class of textbook macroeconomic models that were expanded and fit to data in the 1960s and 1970s in the form of large macroeconometric models like the FRB/MIT/Penn model. In the 1970s, Lucas and others convinced us (though maybe some people were not listening) that those models were not structurally invariant - we should not be using those models to think about policy interventions. The Lucas Critique had its roots in the work of the Cowles Commission (Marschak in particular I think), and it is important. Using the aggregate demand language is (i) not formally correct, either for Farmer, Kocherlakota, Woodford, or Peter Diamond and (ii) It causes backsliding. It was hard enough to convince people in the first instance that the Lucas Critique matters. Now we have to do it all over again. People will do plenty of sloppy economics without any encouragement. We don't want to hand out licenses to do sloppy economics.


  1. There's nothing sloppy about using aggregate demand terminology, and it has nothing to do with the Lucas critique. Traditional formulations of aggregate demand incorporated "sloppy" structural relationships, but getting rid of those does not imply we must discard the terminology. It's useful because it allows us to think about new ideas within a familiar framework, and because it distinguishes one set of ideas from those that influence the supply-side.

  2. I agree that the term aggregate demand can be used well in the right context. For example, in teaching intermediate macro with your textbook, I went through the mechanics of calculating aggregate demand and aggregate supply as a function of prices, and solving for the equilibrium prices for which aggregate demand equals aggregate supply. One could very easily call this solving for the market clearing prices, which is equivalent to solving for prices for which aggregate demand equals aggregate supply in each market.

  3. I'm not sure why you had trouble understanding Farmer's paper. It is laid out very clearly. Think of it this way. With a centralized labor market, the real wage is pinned down by the intersection of labor demand and supply. With search, the labor market need not clear: the labor supply FOC is missing, and we need to add something else to close the model. One thing to add is an explicit bargaining model that effectively pins down the wage. An alternative is to say that output is demand-determined, and that the wage is the marginal product of labor at the demand determined level of output. Then firms are on their labor demand curve, but workers are not on their labor supply curve (but the beauty of search - unemployed workers will take a job at any positive wage). Let me know if you still don't get it (or you think I don't)

  4. Stephen,

    Here is Farmer on indeterminacy and the Lucas Critique:

  5. Anonymous,

    Yes, I know that's what Roger said in the paper, but the words did not make sense in terms of what he actually did. It's that demand language again. It doesn't look to me like demand-determined output. A New Keynesian model literally works like that. A firm with a stuck price is required to produce to satisfy whatever demand arises at that price. In Roger's model there is something called beliefs that go into an inverted Euler equation to determine an asset price. Is that supposed to be the demand?

  6. But surely the concept of an aggregate production function is as invalid as the concepts of aggregate demand ? Why is that any more sound ? I don't think it is - macro as currently practiced is riddled with anomalies. Surely a serious economics must take seriously the idea that the economy is a dense network of connections - Gabaix and Canales is the way of the future.

  7. I don't immediately see how, in effect saying: "... and then everybody wants to buy less stuff" (my translation of "aggregate demand slumps") is "sloppy", although you are right it requires an explanation. There are candidate explanations out there. I think I recall something to do with banks getting in hot water.

    I don't think it makes sense to rule out something (the role of "aggregate demand", as envisaged by those who think it is important) just because your preferred model does not contain anything in it to generate that behaviour. Who says your preferred model is right?

    anybody who is happy swallowing "exogenous productivity shocks" ought to be rather more accommodating of vaguely specified sources of changes in behaviour. This does not entail ignoring the Lucas critique.

  8. An economy always has to satisfy the resource constraint, so the terms production and consumption would seem to be fundamental.

    Is your objection to agg D and S because your decision rule fully describes the equilibrium path of the economy?

  9. My reading of Farmer was that he's just picking an equilibrium from the set of possible solutions. You're right that with Nash bargaining we're back to determinacy, but his paper is more like Bob Hall's wage stickiness work where he chooses to pick another outcome.

  10. "But surely the concept of an aggregate production function is as invalid as the concepts of aggregate demand?"

    That's interesting. Some monetary theorists get bothered when people put money in the utility function (implicit theorizing). Lucas once said that was no worse than writing down a production function (aggregate or not). For some problems we are worried about contractual arrangements within the firm, and what are the boundaries of the firm anyway? I think what you are referring to is the idea that, in a multisectoral economy where the allocation of resources across productive units matters, it does not make sense to be working at the level of an aggregate production function. I think it depends on the question you are trying to ask.

  11. Luis,

    No, for me it doesn't have anything to do with a preferred model. It seems to me that in any modern macro model - New Keynesian, neoclassical growth model, coordination failure, what have you - the AD/AS language is not helpful. That's a language for a particular model. There's no good that can come from trying to ram every other modeling construct into AD/AS by using that language. You end up losing what those other models have to say.

  12. I really don't understand why people insist that AD/AS is useful. What is a shift in AS? Well, TFP say. But that causes an increase in wealth that therefore shifts AD. Oh crap.

    How about G? It shifts AD, right? Except that the taxes required to finance it shift AS via wealth effects on labor supply. Crap, foiled yet again.

    Give me any shock, it moves your "AD" and "AS" curves, however you want to define them. Simply not useful.